Two closed organ pipe A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies `V_(A) and V_(B)` respectively , then

Options

A. `f_(A)=f_(B)`
B. `f_(A)gtf_(B)`
C. `f_(A)ltf_(B)`
D. Either (b) or (c) depending on the ratio of their diameters

Answer

C

Explanation

For closed organ pipe :
End correction = `0.6r=0.3(2r)=0.3d`
For open organ pipe :
End correction : `=1.2r=0.6(2r)=0.6d`
Fundamental mode of vibration of organ pipe
`(lambda)/(4)=(l+0.3d)`
frequency `(f)=(v)/(lambda)=(v)/(4(l+0.3d))`
As l is same, wider pipe A will resonant at lower frequency i.e. `f_(A)ltf_(B)`.